# Complementary Angles, Supplementary Angles & Linear Pair Axiom and its Converse

Complementary Angles: Two angles together are said to be complementary angles if and only if their sum is 90° (Right Angles) and each angle is said to be the complement of the other angles.

For example: – 60° and 30° are complementary angles because 60° + 30° = 90°

Angle complement to 60° is 30° (90° – 60°)

Angle complement to 30° is 60° (90° – 30°)

Supplementary Angles: Two angles together are said to be Supplementary angles if and only if their sum is 180° (Straight Angles) and each angle is said to be the supplement of the other angles.

For example: – 60° and 120° are Supplementary angles because 60° + 120° = 180°

Angle supplement to 60° is 120° (180° – 60°)

Angle Supplement to 120° is 60° (120° – 60°)

Linear Pair Axiom: It states that, if a ray stands on a line, then the sum of adjacent angles so formed is always 180° (Straight Angle). In other words we can say that if a ray stands on a line, the adjacent angles so formed are always supplementary angles.

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In the above figure, we have ∠ACB and ∠ACD are adjacent angles with common arm CA which stands on line BD and common vertex as point C. So,

∠ACB + ∠ACD = 180°

Converse of Linear Pair Axiom: It states that, if the sum of adjacent angles is 180°, then     non-common arms of the angles forms a Straight Line.

In the above figure, if ∠ACB and ∠ACD are adjacent angles with common arm CA such that

∠ACB + ∠ACD = 180°

Then non-Common Arms CB and CD forms a straight line that is ABC is a Straight Line.

Self Assignment:

1. If the measures of two Complementary angles are equal, then find the measure of each angle.
2.  If the measures of two Supplementary angles are equal, then find the measure of each angle.